The theory of radiatively-driven winds successfully explains the key points of the stellar winds of hot massive stars. However, it has been recently found that some O- and B-type stars do not exhibit as strong wind as predicted by theory. In this work we explain the main issues concerning this topic. We also describe our analysis of the UV spectra of a set of massive stars in a Galactic star-forming region (the Orion Complex) plus two reference stars, to determine their wind properties. The wind momentum of the very young OB-stars located in the region and also one of the reference stars are smaller than expected. Our results hint that stellar weak winds may be related to luminosity, rather than age or magnetic fields.